An indirect boundary integral equations method for boundary value problems in elastostatic

In this paper we apply an indirect boundary integral equations method to solve the Dirichlet problem for the n-dimensional linearized elastostatic system in a multiply connected domain of R^n. In particular we show how to represent the solution in terms of a single-layer potential, instead of the usual double-layer potential. As a consequence, we are able to treat also the double-layer potential ansatz for the traction problem. We point out that such method only requires the theory of reducible operators as well as the theory of differential forms.